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On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in S(N)2 Reactions.

ABSTRACT: Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1,2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of S(N)2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment.

SUBMITTER: Rosta E

PROVIDER: S-EPMC3544163 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in S(N)2 Reactions.

Rosta Edina E Warshel Arieh A

Journal of chemical theory and computation 20120329 10

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. Thi ...[more]

PMID: 23329895

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Project description:Linear free energy relationships (LFERs) for substituent effects on reactions that proceed through similar transition states provide insight into transition state structures. A classical approach to the analysis of LFERs showed that differences in the slopes of Brønsted correlations for addition of substituted alkyl alcohols to ring-substituted 1-phenylethyl carbocations and to the β-galactopyranosyl carbocation intermediate of reactions catalyzed by β-galactosidase provide evidence that the enzyme catalyst modifies the curvature of the energy surface at the saddle point for the transition state for nucleophile addition. We have worked to generalize the use of LFERs in the determination of enzyme mechanisms. The defining property of enzyme catalysts is their specificity for binding the transition state with a much higher affinity than the substrate. Triosephosphate isomerase (TIM), orotidine 5'-monophosphate decarboxylase (OMPDC), and glycerol 3-phosphate dehydrogenase (GPDH) show effective catalysis of reactions of phosphorylated substrates and strong phosphite dianion activation of reactions of phosphodianion truncated substrates, with rate constants kcat/Km (M-1 s-1) and kcat/KdKHPi (M-2 s-1), respectively. Good linear logarithmic correlations, with a slope of 1.1, between these kinetic parameters determined for reactions catalyzed by five or more variant forms of each catalyst are observed, where the protein substitutions are mainly at side chains which function to stabilize the cage complex between the enzyme and substrate. This shows that the enzyme-catalyzed reactions of a whole substrate and substrate pieces proceed through transition states of similar structures. It provides support for the proposal that the dianion binding energy of whole phosphodianion substrates and of phosphite dianion is used to drive the conversion of these protein catalysts from flexible and entropically rich ground states to stiff and catalytically active Michaelis complexes that show the same activity toward catalysis of the reactions of whole and phosphodianion truncated substrates. There is a good linear correlation, with a slope of 0.73, between values of the dissociation constants log Ki for release of the transition state analog phosphoglycolate (PGA) trianion and log kcat/Km for isomerization of GAP for wild-type and variants of TIM. This correlation shows that the substituted amino acid side chains act to stabilize the complex between TIM and the PGA trianion and that ca. 70% of this stabilization is observed at the transition state for substrate deprotonation. The correlation provides evidence that these side chains function to enhance the basicity of the E165 side chain of TIM, which deprotonates the bound carbon acid substrate. There is a good linear correlation, with a slope of 0.74, between the values of ΔG‡ and ΔG° determined by electron valence bond (EVB) calculations to model deprotonation of dihydroxyacetone phosphate (DHAP) in water and when bound to wild-type and variant forms of TIM to form the enediolate reaction intermediate. This correlation provides evidence that the stabilizing interactions of the transition state for TIM-catalyzed deprotonation of DHAP are optimized by placement of amino acid side chains in positions that provide for the maximum stabilization of the charged reaction intermediate, relative to the neutral substrate.

Project description:Phosphoryl transfer reactions are ubiquitous in biology and the understanding of the mechanisms whereby these reactions are catalyzed by protein and RNA enzymes is central to reveal design principles for new therapeutics. Two of the most powerful experimental probes of chemical mechanism involve the analysis of linear free energy relations (LFERs) and the measurement of kinetic isotope effects (KIEs). These experimental data report directly on differences in bonding between the ground state and the rate-controlling transition state, which is the most critical point along the reaction free energy pathway. However, interpretation of LFER and KIE data in terms of transition-state structure and bonding optimally requires the use of theoretical models. In this work, we apply density-functional calculations to determine KIEs for a series of phosphoryl transfer reactions of direct relevance to the 2'-O-transphosphorylation that leads to cleavage of the phosphodiester backbone of RNA. We first examine a well-studied series of phosphate and phosphorothioate mono-, di- and triesters that are useful as mechanistic probes and for which KIEs have been measured. Close agreement is demonstrated between the calculated and measured KIEs, establishing the reliability of our quantum model calculations. Next, we examine a series of RNA transesterification model reactions with a wide range of leaving groups in order to provide a direct connection between observed Brønsted coefficients and KIEs with the structure and bonding in the transition state. These relations can be used for prediction or to aid in the interpretation of experimental data for similar non-enzymatic and enzymatic reactions. Finally, we apply these relations to RNA phosphoryl transfer catalyzed by ribonuclease?A, and demonstrate the reaction coordinate-KIE correlation is reasonably preserved. A prediction of the secondary deuterium KIE in this reaction is also provided. These results demonstrate the utility of building up knowledge of mechanism through the systematic study of model systems to provide insight into more complex biological systems such as phosphoryl transfer enzymes and ribozymes.

Dataset Information

On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in S(N)2 Reactions.

Publications

On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in S(N)2 Reactions.

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